43a Mathemat'ual and Philofofihual CorrefpsiukiiCi. 



thing fuppofcd capable of being feparaleil from the body Itfclf. Thus the oJors of bodies 

 •have been fuppofcd to depend on a fubftancc imagined in a loofe way to be common to 

 them all and feparable from them. Hence the terms, principle of fmell, fpiritus roQor ; 

 and even in the modern nomenclature we find arsm,). There does not in ellcc^ fcem to 

 be any more reafon to infer the exiftence of a common principle of fmcU than of tafte. 

 The fmell of ammoniac is the aclion of that gas upon the organ of fenfe ; and this odoraiit 

 Invifible matter is exliibited to the fight when combined with an acid gns. But in the 

 fame manner as ammoniac emanates from water and leaves mod part of that fluid be- 

 hind, fo will the volatile parts of bodies be moll eminently produflive of this action ; and 

 very few, if any> natural bodies will be found which rife totally. The mod ftriking circtim- 

 flance in the cfTeft is, that an a£t of fuch power fhould be attended witli a lofs by exhala- 

 tion which is fcarcely to be appreciated by weight, or in any other method during a 

 fliort interval of time. But we know fo little of nervous action, :ind of other phenomena 

 of eleiilricity, of galvanil'm, or even of heat, which ftrongly alTcd the fcnfes but elude 

 admeafurement by gravitation, that the difficulty of weighing the effluvia of odorant bodies 

 . becomes lefs aftonifhing. 



Question XI. Aofioered hy J. F — : — :— : — R. 



LET H h be tl>e altitudes of the two fignals or other obje£ls, \ their dire£l angular 

 diftaucc, and a their diflerence of azimuth, as flatcd in the queftion. It is proved by the 

 writers on fpheiics, tliat, in any fpherical triangle, Cof. any angle : radius : : radius X cof. 

 oppoCte fide — redlangle cofines including fides : reiflangle fines including fides ; which 

 analogy, applied to the triangle formed by the zenith-diftances and dire£l angular dif- 

 tance of the elevated objefts, gives, Cof. a : radius : : radius X cof. A — fine H X fine h 

 : cof. H X cof. h ; fo that cof. A X radius * = cof. a X cof. H X cof. ^ + fine H X fine h ,• 

 or, putting radius = unity, Cof. a =. cof. a X cof. H X cof. h -J- fine H X fine /•. Q^E. D. 



Question XII. Anfiveredby Mr. William Castjlav, of XJffington, Salop. 



LET Z P O reprefent the zenith, pole, and fun refpe£lively ; x the cof. of ^ PZ (S : 

 then,.per data and a well-known theorem in fpherics, SZ O X S PZ X cof. ^ O ZP -1- 

 cof. Z O X cof. PZ = cof. P O ("fl being i) ; that is (putting d for fine of the fun's dec. 

 Ijo 9' or .26135) * X A- X * + I — .v.r = d : this equation ordered is k' — ** = </— I 

 = _ .73865, whence x = — .66588 — cof. 131° 45' .-. 48° 15' will be the azim. when 

 equal to the lat. and alt. on the given day. The /. ZP © alfo = 2'' 3 '54". Per Naut. Aim. 

 the fun's declination for noon, on tlie given day (at Greenwich), is 15° 18' 28", and its 

 change for 24"" = i8' 7" .-. As 18' 7' : 24" :: 15" iK'28"— 15° 9': 1%" 32' 27" the 

 time from noon at Greenwich when the obfervation was made. The latitude of the 

 place of obfervation, then, is 48° 15' N. and its longitude (12" 32' 27" — 2" 3' 54") 

 10'" 28' 33" E. of Greenwich. 



t^" The fame was anfwered by J. F—: — ; 



